To date, an engine automatic-stop/restart system has been developed for the purpose of improving the gasoline mileage of a vehicle such as an automobile and reducing an environmental load. When due to a driver's operation, a predetermined condition (e.g., brake-on operation under a predetermined vehicle speed or lower) for stopping an engine is satisfied, an engine automatic-stop/restart system automatically cuts off the fuel so as to automatically stop the engine. After that, when due to the driver's operation, a predetermined condition (e.g., brake-releasing operation, accelerator pedal step-on operation, or the like) for restarting the engine is satisfied, the engine automatic-stop/restart system restarts fuel injection so that the engine is automatically restarted.
As such an engine automatic-stop/restart system, for example, in the method of making a starter pinion gear engage with a ring gear and a starter control apparatus disclosed in Patent Document 1, a rotation orbit along which the rotation speed becomes zero is estimated based on the engine rotation speed obtained from a crank pulse; from the estimated rotation orbit, there is estimated a timing at which the rotation speed becomes zero; then, the estimated timing is periodically monitored and at a time when a driving timing is reached, the starter is driven.